Sphere On Plate

 

BACKGROUND
     Another name for this analysis is the Hertzian Indentation.  In this project, a steel ball is pressed into a plate surface.  We want to obtain the distribution of the contact stresses.   To solve this problem without a computer,  theories would have to be employed and the solution would be limited to elastic materials only.  Also, the type of load applications for these theories were limited to point loads and distributed loads.   However, in the modern world, we can use Finite Element Analysis (FEA) packages to obtained the stress distribution for elastic-plastic materials with a variety of loadings and constraints.  Furthermore, the finite element solution can be much more accurate than the theoretical solution, if setup properly.  One popular FEA software package is ANSYS.  ANSYS allows us to import geometries or to  make them from within ANSYS, apply loading and constraints, and then solve for a solution.  Then the desired quantities (stress, strain, DOF) can be plotted from the solution.

PROCEDURE
    For this project, the solution was done in stages.  The analysis of the sphere and plate can be done in two-dimensions or three-dimensions.  Also, ANSYS has the ability to show crack initiation and propagation for brittle materials.  Based on what ANSYS can do, the stages of the project were broken up as follows:
  1st Stage - 2D analysis
  2nd Stage - 2D analysis with crack propagation
  3rd Stage - 3D analysis
 

RESULTS
    In each stage, the results help show how the tensile stresses on the surface of a brittle plate could cause crack initiation and crack propagation.  In the slide show, there are animations which show this crack propagation.
There are several highlights of the results that need to be noted:
1. Compressive stresses at the contact point between the sphere and plate
2. High tensile stresses on plate surface
3. For brittle materials (Dicor/MGC), the tensile stresses act as initiation site for crack propagation (Crack propagation can be seen in 2nd Stage Results)

    For the 2nd Stage results the crack is shown initiating and then propagating downward into the plate at about a 20^o angle with the horizontal.  Also as the crack propagates, the stresses in at the crack tip dissipate.  Another thing to note is that the mesh for the 2D analysis is finer that the 3D analysis.  This is because the student version of ANSYS is limited to 10,000 elements.  Therefore, because the 3D model requires more elements, they are space out more to stay below 10,000 elements total.  This results in an solution that is not as accurate as the 2D analysis, however it is close enough to notice the similarity between the 2D and 3D analysis.
 
 

Slideshow - Table of Contents ANSYS Analysis  Group 5  Project Goals - Hertizan Indentation Model  2D analysis of stress  2D analysis of stress (2)  2D analysis of stress with crack propagation  2D analysis of stress with crack propagation (2)  3D analysis of stress  3D analysis of stress (2)  3D analysis of stress (3)  3D analysis of stress (4)  Applications of Analysis  Closing Points

For problems or questions regarding this web page contact [daveware@wam.umd.edu].
Last updated: Dec 12, 1998.